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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Determinants

NDA 2015 · Mathematics · Determinants

The matrix A=[ array ccc 1 & 3 & 2 1 & x-1 & 1 2 & 7 & x-3 array ]...

The matrix \mathrm{A}=\left[1321x−1127x−3\begin{array}{ccc}1 & 3 & 2 \\ 1 & x-1 & 1 \\ 2 & 7 & x-3\end{array}\right] will have inverse for every real number xx except for

Options

  1. Ax=11±52x=\frac{11 \pm \sqrt{5}}{2}
  2. Bx=9±52x=\frac{9 \pm \sqrt{5}}{2}
  3. Cx=11±32x=\frac{11 \pm \sqrt{3}}{2}
  4. Dx=9±32x=\frac{9 \pm \sqrt{3}}{2}

Correct answer

A. x=11±52x=\frac{11 \pm \sqrt{5}}{2}

Step-by-step solution

A=\left[1321x−1127x−3\begin{array}{ccc}1 & 3 & 2 \\ 1 & x-1 & 1 \\ 2 & 7 & x-3\end{array}\right]∣A∣=1[(x−1)(x−3)−7]−3[(x−3)−2]+2[7−2(x−1)]=x2−11x+29\begin{aligned} & |A|=1[(x-1)(x-3)-7]-3[(x-3)-2]+2[7-2(x-1)] \\ & =x^2-11 x+29 \end{aligned}If inverse will not exist then $|\mathrm{A}|=0\begin{aligned} & \mathrm{x}^2-11 \mathrm{x}+29=0 \\ & \mathrm{x}=\frac{11 \pm \sqrt{5}}{2} \end{aligned}$$$
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